using new URL to access web app

We are switching internet domains at work, but the old domain is not going away, given the legacy support required (AD domain is also not changing). I have a small (1 SP server, 1 SQL server) SP2013 SP1 farm which I would like to have people access with the new domain. So e.g. the SP web app currently lives at portal.mycompany.com and I want people to access it at newportal.newcompany.com. It looked like Alternative Access Mappings would be the ticket but I am not seeing how to utilize that, if it is even possible. Suggestions?